A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses. (i) A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is : (ii) A double-convex lens of power P, with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be : (iii) The above two parts are kept in contact with each other as shown in the figure (two plano-convex halves touching, forming a double-convex shape). The power of the combination will be : (iv)(a) A double-convex lens of power P, with each face having same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure (two halves placed side by side above the axis). The power of the combination will be : (iv)(b) Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each other. The power of the combination is :

PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 4 marks · Case-based

CBSE Class 12 Physics 2024: question 29

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section D, question 29, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 4 marks · Case-basedCompetency-basedRay Optics and Optical Instruments

A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.

(i)
A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is :
1. (A) $\frac{2 ( n - 1 )}{R}$
2. (B) $\frac{( 2 n - 1 )}{R}$
3. (C) $\frac{( n - 1 )}{2 R}$
4. (D) $\frac{( 2 n - 1 )}{2 R}$
1 mark
(ii)
A double-convex lens of power P, with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be :
1. (A)2P
2. (B)P
3. (C)4P
4. (D) $\frac{P}{2}$
1 mark
(iii)
The above two parts are kept in contact with each other as shown in the figure (two plano-convex halves touching, forming a double-convex shape). The power of the combination will be :
1. (A) $\frac{P}{2}$
2. (B)P
3. (C)2P
4. (D) $\frac{P}{4}$
1 mark
(iv)(a)
A double-convex lens of power P, with each face having same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure (two halves placed side by side above the axis). The power of the combination will be :
1. (A)Zero
2. (B)P
3. (C)2P
4. (D) $\frac{P}{2}$
1 mark
OR
(iv)(b)
Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each other. The power of the combination is :
1. (A)6.6 D
2. (B)15 D
3. (C) $\frac{1}{15}$ D
4. (D) $\frac{1}{80}$ D
1 mark

Figure in the paper: Figure in (iii): two plano-convex halves in contact along the principal axis forming a double-convex lens shape. Figure in (iv)(a): two lens halves arranged side by side on one side of the principal axis. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Use the lens maker's formula with $R_{1} = R$ and $R_{2} = - R$ .

Hint 2

A cut perpendicular to the axis removes one curved face; a cut along the axis keeps both faces.

Hint 3

For lenses in contact, powers add: $P = P_{1} + P_{2}$ , with f in metres.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) $P = \frac{1}{f} = (n - 1) (\frac{1}{R} - \frac{1}{- R}) = \frac{2 ( n - 1 )}{R}$ . Option (A).
1 mark
(ii) Cutting perpendicular to the axis gives two plano-convex halves, each with $P^{'} = \frac{( n - 1 )}{R} = \frac{P}{2}$ . Option (D).
1 mark
(iii) The two halves in contact give $P_{n e t} = \frac{P}{2} + \frac{P}{2} = P$ . Option (B).
1 mark
(iv)(a) A cut along the principal axis leaves both curved faces on each half, so each half keeps power P. Placed one after the other along the axis, as in the figure, they give $P + P = 2 P$ . Option (C).
1 mark
(iv)(b) $P = \frac{1}{0.60} + \frac{1}{0.20} = 1.67 + 5 = 6.67 D \approx 6.6$ D. Option (A).

Answer: (i) A; (ii) D; (iii) B; (iv)(a) C; (iv)(b) A

Where the marks are

(i) $2 (n - 1) / R$ – option A (1 mark)
(ii) P/2 – option D (1 mark)
(iii) P – option B (1 mark)
(iv)(a) 2P – option C, or (iv)(b) 6.6 D – option A (1 mark)

Revise the chapter

Chapter: Ray Optics and Optical Instruments (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Ray Optics and Optical Instruments, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2024: question 29

Hints

Step-by-step solution

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